# User:Jaroslaw Karcz/Modelling Sandbox

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(→THE KEY) |
Current revision (22:41, 6 December 2007) (view source) (→THE KEY) |
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==THE KEY== | ==THE KEY== | ||

- | <math>\nabla \times \nabla \times v = ...</math><br> | + | <math>\nabla \times \nabla \times v = ...</math><br><br> |

+ | <math>\nabla \times v = \epsilon_{spq}v_{q,p}</math><br> | ||

+ | <math>\nabla \times \nabla \times v = \epsilon_{irs}(\epsilon_{spq}v_{q,p})_{,r}</math><br><br> | ||

<math>\Rightarrow \epsilon_{irs} \epsilon_{spq} (v_{q,p})_{r}</math><br> | <math>\Rightarrow \epsilon_{irs} \epsilon_{spq} (v_{q,p})_{r}</math><br> | ||

<math>\Rightarrow \epsilon_{sir}\epsilon_{spq}v_{q,pr}</math>....cyclic permutation<br> | <math>\Rightarrow \epsilon_{sir}\epsilon_{spq}v_{q,pr}</math>....cyclic permutation<br> |

## Current revision

## Contents |

## THE KEY

....cyclic permutation

...continuous function

#### Convert to vector notation

## Model Development

The process of modelling consists of a number of layers; the following is a description of the modelling workflow:

**Definition of the problem****Verification of information available****Selection of model structure****Establishing a simple model****Sensitivity analysis****Experimental tests of the model predictions****Stating the agreements and divergences between experimental and modelling results, including any emergent behaviour****Iterative refinement of model**

## Introduction

The real world is dominated by complexity, especially biological systems

Mathematical modelling and computer simulations provide a means of understanding the innate funtioning of system - dynamics, and to arrive at well-founded predictions about their future development and the effect of interactions with the environment.
So what is a model? A model is an abstract representation of objects and processes that explain the features/nature of these objects or processes. We present the model of our construct, as a system of differential equations to describe the dynamics of that network.

## Model Parameters

Parameter | Value | Description | Comment (literature, derived?) |
---|---|---|---|

k_{1}
| x [units] | max. transcription rate of constitutive promoter (pTET) | Estimate |

k_{2}
| |||

k_{3}
| |||

k_{4}
| |||

k_{5}
| |||

k_{6}
| x [units] | ||

δ_{GFP}
| 0.029 hrs ^{-1}
| degradation rate of GFP | Literature ~~ give reference |